Peter Shalen
Peter B. Shalen (born July 23, 1946 in New York City ) is an American mathematician who studies geometric topology . He is a professor at the University of Illinois at Chicago .
Shalen graduated from Stuyvesant High School in 1962 and graduated from Harvard University with a bachelor's degree in 1966, studied one year 1966/67 at the École normal supérieure and received his doctorate in 1972 from Harvard under Edwin Moise ( A piecewise linear proof for triangulation theorem of 3-manifolds ). From 1971 to 1974 he was JF Ritt Assistant Professor at Columbia University and from 1974 to 1979 Assistant Professor , 1979 Associate Professor and 1983 Professor at Rice University . Since 1985 he has been a professor at the University of Illinois in Chicago .
He was visiting scholar at the Courant Institute (1978/79), at Columbia University (1981/82), at the University of Nantes, the University of Paris-South, at the MSRI (1985), at the University of Toulouse (Paul Sabatier), the University of Chicago (1998/99), the University of Paris and the Université de Bourgogne.
In 1987 he proved the Cyclic Surgery Theorem with Marc Culler , John Edwin Luecke and Cameron Gordon . The JSJ decomposition of 3-manifolds is named after him, William Jaco (with whom he published about it) and Klaus Johannson .
He was involved in the solution of the Smith Conjecture (drawn up by Paul A. Smith ). With John Morgan he gave new evidence on a number of William Thurston's fundamental findings .
In 1986 he was invited speaker at the International Congress of Mathematicians in Berkeley (Representations of 3-manifold groups and applications in topology). From 1992 to 1997 he was the editor of Geometric Topology . From 1977 to 1979 he was a Sloan Research Fellow .
Fonts
- with William H. Jaco: Seifert fibered spaces in 3-manifolds (= Memoirs of the American Mathematical Society. 220). American Mathematical Society, Providence RI 1979, ISBN 0-8218-2220-9 .
- with William H. Jaco: Seifert fibered spaces in 3-manifolds. In: James C. Cantrell (Ed.): Geometric topology. Proceedings of the 1977 Georgia Topology Conference, Athens, Ga., Aug. 1-12, 1977. Academic Press, New York NY et al. 1979, pp. 91-99.
- Separating, incompressible surfaces in 3-manifolds. In: Inventiones Mathematicae . Vol. 52, 1979, pp. 105-126 .
- with Marc Culler: Varieties of group representations and splittings of 3-manifolds. In: Annals of Mathematics . Volume 117, number 1, 1983, pp. 109-146, doi : 10.2307 / 2006973 .
- with John W. Morgan: Valuations, trees, and degenerations of hyperbolic structures, I. In: Annals of Mathematics. Volume 120, Number 3, 1984, pp. 401-476, doi : 10.2307 / 1971082 .
- with Marc Culler, Cameron McA. Gordon, John Luecke: Dehn surgery on knots. In: Annals of Mathematics. Volume 125, Number 2, 1987, pp. 237-300, doi : 10.2307 / 1971311 .
- with John W. Morgan: Degenerations of hyperbolic structures, II: Measured laminations in 3-manifolds. In: Annals of Mathematics. Volume 127, Number 2, 1988, pp. 403-456, doi : 10.2307 / 2007061 .
- with John W. Morgan: Degenerations of hyperbolic structures, III: Actions of 3-manifold groups on trees and Thurston's compactness theorem. In: Annals of Mathematics. Volume 127, Number 3, 1988, pp. 457-519, doi : 10.2307 / 2007003 .
- with Daryl Cooper, Marc Culler, Henri Gillet , Darren D. Long: Plane curves associated to character varieties of 3-manifolds. In: Inventiones Mathematicae. Volume 118, 1994, pp. 47-84 .
Web links
Individual evidence
- ^ Mathematics Genealogy Project , the title of the dissertation after Edwin Evariste Moise: Geometric topology in dimensions 2 and 3 (= Graduate Texts in Mathematics. 47). Springer, New York NY et al. 1977, ISBN 0-387-90220-1 .
- ↑ Culler, Gordon, Luecke, Shalen: Dehn surgery on knots. In: Annals of Mathematics. Volume 125, 1987, pp. 237-300.
| personal data | |
|---|---|
| SURNAME | Shalen, Peter |
| ALTERNATIVE NAMES | Shalen, Peter B. |
| BRIEF DESCRIPTION | American mathematician |
| DATE OF BIRTH | July 23, 1946 |
| PLACE OF BIRTH | New York City |